Common methods for operating laser cutting machines perform two-dimensional (2D) relative motion between a laser beam and a workpiece, such that the laser beam cuts the workpiece as the beam moves. In such machines, there are three options. A position of the laser is fixed and the workpiece is moved in X and Y directions. A position of the workpiece is fixed and the laser or a mirror in the beam path is moved in the X and the Y directions. The laser is fixed in the Y direction and the beam in the X direction, and the workpiece is fixed in X direction and moves in Y direction.
A limiting factor on the production rate of electromechanical machine, such as laser cutting machines, is directly related to the inertia of the components of the laser-cutting machine. Therefore, reduction of the effective inertia of the components has a direct impact on the productivity of the laser-cutting machine. Such reduction can be achieved by using redundant actuators along each direction of the motion.
For example, one laser cutting machine uses a pair of redundant actuators along the direction of the motion, i.e., a planar gantry with a high inertia and a polar gantry with a low inertia. However, the inertia of the laser even in this machine is still relatively large, as the laser-focusing lens itself is moved. Such motion also stresses the precision optics of the laser-focusing lens and may lead to a suboptimal cut.
Another possible method of reducing inertia is to replace the X-Y motion completely with a pair of mirrors moved by galvano drives. With a suitable choice of lenses and lasers, these XY galvano assemblies can be used in the machine with redundant actuators as beam directors, or as laser engraving devices.
For example, one machine with redundant actuators places the XY galvano scanhead on the end of a multi-axial industrial robot arm. The path of the robot end is then constrained to stay within a “mobility tube” describing the set of positions where the galvano scanhead is capable of aiming at the area to be machined. The correct set of multi-axial robot joint motions, combined with the proper galvano drive signals are dynamically determined by the control unit.
However, avoidance of “robot arm crashes” in this design, i.e., situations where the robot arm tries to pass through itself or through the workpiece, is computationally difficult, and requires not only an accurate model of the robot arm and scanhead, but also a continuously evolving model of the workpiece during different stages of the cutting process, because a forbidden motion at one stage in the cutting process may be available for another stage of the process. Accordingly, controlling the machine with redundant actuators is a challenging problem.
For example, in one method for controlling redundant actuators, i.e., a fast actuator and a slow actuator, the coordinated control of the redundant actuators is achieved by frequency separation. Because the slow actuator travels large ranges of motion at relatively low speeds when compared with the fast actuator, the slow actuator cannot follow the high frequency components of the reference trajectory. Accordingly, the reference trajectory is processed by low and high pass filters, such that the output of the low pass filter is submitted to the slow actuator and the output of the high pass filter is submitted to the fast actuator. However, that method does not explicitly handle the position constraints of the fast actuator. Too low a cut off frequency results in fast actuator position constraint violations. On the other hand, too high a cut-off frequency results in slow actuator carrying out most of the cutting motions, thus defeating the purpose of the frequency separation method.
In another method for controlling redundant actuators in a laser cutting machine, a pseudo-inverse of a Jacobian matrix of the redundant configuration is used to compute joint profiles needed to position the fast actuator. That method only accounts for kinematics of the system while neglecting the dynamics of the actuators. Moreover, there are no guarantees that physical constraints of the actuators are violated, which can lead to the situations where the slow actuator moves beyond the range of the fast actuator and the error in tracking the reference trajectory becomes unbounded.
Accordingly, there is a need to overcome the disadvantages described above.